CLOCK - Editorial

CLOCK:

DIFFICULTY:

PREREQUISITES:

PROBLEM:

Given time in HH MM SS format and you have to find what will be time after hour hand moves by x degrees.

EXPLANATION:

If hour hand moves by 1 degree then 2 minutes will happen in 12 hour clock. As x is integer and smallest change in x can be only 1 degree hence
second hand will come to its original position whatever may be the value of x i.e SS field will not change.
Now find if minutes to add in MM field is greater than 60 or not . If final MM field > 60 then add extra minutes in hour by converting minutes to
hour.

Note : if x > 360 that means hour hand has moved by more than 360 degrees i.e several complete rotations have happened.
so to solve one can do x = x%360 which will have same effect.

The preliminary step here is to find out what $1$ degree motion of the hour hand means in terms of time. 0ne full rotation of the hour hand is $12$ hours or $12\times 60 = 720$ minutes, and conveniently we have $720/360 = 2$ exactly; giving $2$ minutes per degree.

If, instead of degrees, the question had asked the time after the hour hand is moved by $x$ gradians, which have $400$ for a full turn, we would have had to go down to an effect in seconds, with $720\times 60 = 43200$ second in a full turn of the hour hand and thus $108$ seconds per gradian.

@joffan Thanks for your suggestion about use of gradians in problem . But I wanted to design an easy problem So I deliberately made a special case in which that it turns out that 1 degree corresponds to 2 minutes.